# Seminario di Equazioni Differenziali e Applicazioni: “Nonlinear Schrödinger ground states on metric graphs: the $L^2$-critical case”

## Mercoledì 25 Gennaio 2017, ore 12:15 - Aula 2BC30 - Enrico Serra

ARGOMENTI: Seminari

Mercoledì 25 Gennaio 2017 alle ore 12:15 in Aula 2BC30, Enrico Serra (Politecnico di Torino) terrà un seminario dal titolo “Nonlinear Schrödinger ground states on metric graphs: the $L^2$-critical case”.

Abstract
We investigate the existence of ground states with prescribed mass for the focusing nonlinear Schrödinger equation with $L^2$-critical power nonlinearity on noncompact quantum graphs. We prove that, unlike the case of the real line, for certain classes of graphs there exist ground states with negative energy for a whole interval of masses. A key role is played by a thorough analysis of Gagliardo-Nirenberg inequalities and by estimates of the optimal constants. Most of the techniques are new and suited to the investigation of variational problems on metric graphs.

Rif. Int. M. Bardi, C. Marchi, F. Rampazzo